Is Q-learning a type of model-based RL?
Tabular Q-Learning does not explicitly create a model of the transition function. It does not generate any output that you can afterwards use as a function to predict what the next state s' will be given a current state s and an action a (that's what a transition function would allow you to do). So no, Q-learning is still model-free.

By the way, model-based RL does not necessarily have to involve creating a model of the transition function. Model-based RL can also mean that you assume that such a function is already given. It just means that you use such a function in some way.